I tend to interpret many as a relative term, meaning "a high number relative to what you're probably expecting". The dictionary is no help here as it just defines many as "a lot", but that in turn is also a relative term.
I think if you want to argue with this point, a better tack would be to argue that the British PM is underpaid and EU staff are what "normal" compensation should look like. Quibbling over whether 10% of them being paid more qualifies as a lot isn't that worthwhile.
Being in the situation of currently enjoying* the UK PM's leadership, I'd be more inclined to argue the other way.
(Although, in a more serious tone, I would argue that long-term high level civil servants probably do deserve a higher wage than transients like PM, President, Cabinet Minister, etc.)
As a raw number, sure, 4000 is "many" but 10% is not really "many of whom" (which is what GP said) - for me, obviously; other people's interpretation may vary.
(e.g. If I said "there's some cats outside; many of them are blue" but only 10% are blue, I would expect people to query the "many".)